TI-BASIC:Inverse
Command Summary
Returns the reciprocal of a number (1 divided by the number). For matrices, finds the matrix inverse.
Command Syntax
valueֿ¹
Menu Location
Press [xֿ¹]
TI-83/84/+/SE
1 byte
The ֿ¹ command returns the reciprocal of a number, equivalent to dividing 1 by the number (although reciprocals are sometimes more convenient to type). It also works for lists, by calculating the reciprocal of each element.
The ֿ¹ command can also be used on matrices, but it is the matrix inverse that is computed, not the reciprocal of each element. If [A] is an N by N (square) matrix, then [A]ֿ¹ is the N by N matrix such that [A][A]ֿ¹=[A]ֿ¹[A] is the identity matrix. ֿ¹ does not work on non-square matrices.
4ֿ¹ .25 {1,2,3}ֿ¹ {1 .5 .3333333333} [[3,2][4,3]]ֿ¹ [[3 -2] [-4 3 ]]
Much like the number 0 does not have a reciprocal, some square matrices do not have inverses (they are called singular matrices) and you'll get an error when you try to invert them.
Optimization
Writing Aֿ¹B instead of B/A is sometimes beneficial when B is a complicated expression, because it allows you to take off closing parentheses of B. For example:
:(P+√(P²-4Q))/2 can be :2ֿ¹(P+√(P²-4Q
This may be slower than dividing. There are also situations in which this optimization might lose precision, especially when the number being divided is large:
7fPart(4292/7 1 7fPart(7ֿ¹4292 .9999999999
Error Conditions
- ERR:DIVIDE BY 0 is thrown when trying to take the reciprocal of 0.
- ERR:SINGULAR MAT is thrown when trying to invert a singular matrix.